Ordered one off Amazon and it got here pretty sharpish. I've got an old plug and length of 2x0.75mm flex from a small appliance I can use to power the thermostat. It does indeed keep it's memory, but only after you go back off the settings screen - if you stay on the settings screen it seems to forget everything if unplugged! It also differs to bigclive's video, there is no transformer, it has mains, directly through a diode on one of the legs, into a small SOIC8 (I'm getting old, I couldn't read the number). There is a good 10mm between mains in and the thermistor although there is no clearance cutout. I printed an enclosure for it, and made some holes for PG cord grips to fit.
My plan is to pull the fridge/freezer out, unscrew the black cowl over the connections, find the two brown wires that go up to the fridge thermostat/light and break them, using a couple of 3-way Wagos to connect everything back up. I've got a length of 2x1.5mm flex for the relay connection to the STC-1000. I believe this should mean the original thermostat will kick in if the STC-1000 for some reason does not (memory lost, or relay failure). The thermistor for now will snake through the door seal into the fridge, so I can figure out the best place for it, and once I've figured that out, I'll see if I can fish something down the cable route from the existing thermostat and pull it through there, or gingerly make a hole through the fridge body.
I also found a diagram for the Ranco thermostat adjustment screws! Success.... or so I thought. The one screw adjusts the "cut in" temp, and the dial in the fridge appears to adjust the "cut out" temp. If you have too short of a range between the two, and the cut in too low, the fridge may stay cold, but the freezer starts to warm up! Interesting. I believe the thermostat also measures the cold plate in the fridge rather than the fridge temp itself, so that, accompanied by the low ambient temps, the fridge just stays too cold. Lots of videos online of people installing "winter heaters" and "garage heaters", or leaving the bulb on in the fridge..... but I also wonder if the end of the thermistor sense tube is actually in the right place, it's some 15 years old and it's been moved around a lot in its life.